Batch Distillation With Holdup

Batoh distillation is frequently used for small-volume products. One column can be used to separate a multicomponent mixture instead of requiring NC — 1 continuous colimms. The energy consumption in batch distillation is usually higher than in continuous, but with small-volume, high-value products energy costs seldom dominate the economics. 

The eolunin is run on total reflux until the overhead distillate eomposition of the lightest component (component 1) reaches its specification purity. Then a distillate product, which is the lightest component, is withdrawn at some rate. Eventually the amount of eomponent 1 in the still pot gets very low and the Xdi purity of the distillate drops. There is a period of time when the distillate contains too little of component 1 to be used for that product and also too little of component 2 to be used for the next heavier product. Therefore a slop cut must be withdrawn until Xj)2 builds up to its specifieation. Then a seeond product is withdrawn. Thus multiple produets can be made from a single eolumn. 

Theoretical trays, equimolal overflow, and constant relative volatilities are assumed. The total amount of material charged to the column is M q (moles). This material ean be fresh feed with composition Zj or a mixture of fresh feed and the slop cuts. The composition in the still pot at the begiiming of the batch is Xgoj. The composition in the still pot at any point in time is Xgj. The instantaneous holdup in the still pot is Mg. Tray liquid holdup and reflux drum holdup are assumed constant. The vapor boilup rate is constant at V (moles per hour). The reflux drum, eolumn trays, and still pot are all initially filled with material of eomposition Xg j. 

The eontrol of pH is a very important problem in maity processes, particularly in effluent wastewater treatment. The development and solution of mathematical models of these systems is, therefore, a vital part of chemical engineering dynamic modeling. 

---

A detailed differential stepwise integration for a batch distillation with holdup can be made, but the time and effort involved are usually not justified by the value of the result. The method is useful in developing the principles of batch distillation with holdup. The following section will consider the basic differential equations which are helpful in obtaining a qualitative picture of the process. By an analysis similar to that for Eq. (14-1),... 

Consider the binary batch distillation column, represented in Fig. 3.58, and based on that of Luyben (1973, 1990). The still contains Mb moles with liquid mole fraction composition xg. The liquid holdup on each plate n of the column is M with liquid composition x and a corresponding vapour phase composition y,. The liquid flow from plate to plate varies along the column with consequent variations in M . Overhead vapours are condensed in a total condenser and the condensate collected in a reflux drum with a liquid holdup volume Mg and liquid composition xq. From here part of the condensate is returned to the top plate of the column as reflux at the rate Lq and composition xq. Product is removed from the reflux drum at a composition xd and rate D which is controlled by a simple proportional controller acting on the reflux drum level and is proportional to Md-... 

Operation of a batch distillation is an unsteady state process whose mathematical formulation is in terms of differential equations since the compositions in the still and of the holdups on individual trays change with time. This problem and methods of solution are treated at length in the literature, for instance, by Holland and Liapis (Computer Methods for Solving Dynamic Separation Problems, 1983, pp. 177-213). In the present section, a simplified analysis will be made of batch distillation of binary mixtures in columns with negligible holdup on the trays. Two principal modes of operating batch distillation columns may be employed ... 

In a steady state continuous distillation with the assumption of a well mixed liquid and vapour on the plates, the holdup has no effect on the analysis (modelling of such columns does not usually include column holdup) since any quantity of liquid holdup in the system has no effect on the mass flows in the system (Rose, 1985). Batch distillation however is inherently an unsteady state process and the liquid holdup in the system become sinks (accumulators) of material which affect the rate of change of flows and hence the whole dynamic response of the system. 

Reprinted from Chem. Eng. Sci., 53, Mujtaba, I.M. and Macchietto, S., Holdup issues in batch distillation-binary mixture, 2519-2530, Copyright (1998), with permission from Elsevier Science. ... 

Seader and Henley (1998) considered the separation of a ternary mixture in a batch distillation column with B0 = 100 moles, xB0 = = <0.33, 0.33, 0.34> molefraction, relative volatility a= <2.0, 1.5, 1.0>, theoretical plates N = 3, reflux ratio R = 10 and vapour boilup ratio V = 110 kmol/hr. The column operation was simulated using the short-cut model of Sundaram and Evans (1993a). The results in terms of reboiler holdup (Bj), reboiler composition profile (xBI), accumulated distillate composition profile (xa), minimum number of plates (Nmin) and minimum... 

Converse and Huber (1965), Robinson (1970), Mayur and Jackson (1971), Luyben (1988) and Mujtaba (1997) used this model for simulation and optimisation of conventional batch distillation. Domenech and Enjalbert (1981) used similar model in their simulation study with the exception that they used temperature dependent phase equilibria instead of constant relative volatility. Christiansen et al. (1995) used this model (excluding column holdup) to study parametric sensitivity of ideal binary columns. 

A liquid binary mixture with Bo = 10 kmol and xbo = <0.6, 0.4> molefraction is subject to conventional batch distillation shown in Figure 4.3. The relative volatility of the mixture over the operating temperature range is assumed constant with a value of (a=) 2. The total number of plates is, N = 20. The vapour boilup rate is, V = 5.0 kmol/hr and the reflux ratio is, r = 0.75. The condenser and total plate holdups are 0.2 and 0.2 kmol respectively. 

Nad and Spiegel (1987) carried out experimentation in a conventional packed batch distillation column using a cyclohexane-heptane-toluene mixture. The column consists of 20 theoretical stages (equivalent) including the condenser and reboiler. The feed to the column was 2.93 kmol of which 1.9% was total column holdup and 1.2% was condenser holdup. The column underwent an initial total reflux operation for about 2.54 hr before any product was collected. After then the mixture was separated into 3 main-cuts with 2 off-cuts in between, leaving a final product in the reboiler. 

Robinson (1970) considered an industrial 10-component batch distillation operation. The feed condition is shown in Table 5.3. The distillation column was currently producing the desired product using constant reflux ratio scheme. Table 5.4 summarises the results of the application of minimum time problem using simple model with and without column holdup. 

For single separation duty, Diwekar et al. (1989) considered the multiperiod optimisation problem and for each individual mixture selected the column size (number of plates) and the optimal amounts of each fraction by maximising a profit function, with a predefined conventional reflux policy. For multicomponent mixtures, both single and multiple product options were considered. The authors used a simple model with the assumptions of equimolal overflow, constant relative volatility and negligible column holdup, then applied an extended shortcut method commonly used for continuous distillation and based on the assumption that the batch distillation column can be considered as a continuous column with changing feed (see Type II model in Chapter 4). In other words, the bottom product of one time step forms the feed of the next time step. The pseudo-continuous distillation model thus obtained was then solved using a modified Fenske-Underwood-Gilliland method (see Type II model in Chapter 4) with no plate-to-plate calculations. The... 

The batch distillation column consisted of 3 internal plates, reboiler and a total condenser. The reboiler was charged with a fresh feed of 5 kmol with Benzene molefraction 0.6. The total column holdup was 4 % of the charge. Half the holdup was in the condenser and the rest was distributed over the plates. The vapour load to the condenser was 3 kmol/hr. The required product purities were x oi = 0.90 and x B2 = 0.15. The solution of Equations 8.1-8.4 therefore gives DJ = 3.0 kmol and B2 = 2 kmol. This problem is same as case 3 shown in Table 8.1. Three reflux ratio (control) intervals were used to achieve (Dl, x Di) and one control interval to achieve (B2, x B2). 

It is important to note that in using computer-aided models for batch distillation, the various assumptions of the model can have a significant impact on the accuracy of the results e.g., see the discussion of the effects of holdup above. Uncertainties in the physical and chemical parameters in the models can be addressed most effectively by a combination of sensitivity calculations using simulation tools, along with comparison to data. The mathematical treatment of stiffness in the model equations can also be very important, and there is often a substantial advantage in using simulation tools that take special account of this stiffness. (See the 7th edition of Perry s Chemical Engineers Handbook for a more detailed discussion of this aspect). 

---